Drawabox 250 box challenge: gaining further insights

In lieu of my drawing warm-ups today, since I'm short on time and need to code, I'm doing some quick research on how to get the most bang for my buck in the Drawabox 250 Box Challenge. 

I'm only about 35 boxes in, and I'm on the struggle bus. Recently, I have had a few questions about it. 

• What exactly is the full purpose of drawing the colored lines on each finished page of boxes? 
• What is the benefit of avoiding any sort of parallel lines on my boxes, and moreover, how exactly do I even do that without completely distorting my boxes? 

So I reread the article and did some speculating and thinking. 

What I gathered: the goal of the colored line extensions is to have them eventually all meet at the same point. No crossing over each other, or spiraling out into weird directions. Even if you don't have enough room on your paper to measure this, it's what would happen if you theoretically had unlimited paper. So you basically just have to visualize it. 

For the parallel lines question: the lines are supposed to represent something that is parallel without actually being parallel. Actually, if you visualize the vanishing points and corresponding line extensions before actually drawing them, then you can see that parallel lines don't really make sense. My problem was that I was thinking about boxes in terms of how I drew them in elementary school (i.e. this line goes down, then draw the next line connected to it) instead of in terms of where vanishing points should be extended to. 

There are basically two components to getting this working: properly visualizing, an inherently mental exercise, and proper execution, an inherently physical exercise. I struggle with both, but I've got time. I'll get it down. I will have to think about this again while actually drawing, I think, for it to fully solidify in my mind.